The announcement by U.S. State Department officials that the USSR had agreed to settle the cases of 36 divided families, one separated spouse and one dual national was certain to set hundreds of households on edge.

``We`re always the last to find out,`` said one Soviet woman whose American-born husband returned to his native California last week when a guest visa expired.

The woman, who requested anonymity, said it can take weeks before the authorities responsible for issuing visas notify those whose departure has been authorized.

``The Soviet government tells your State Department, and the State Department tells your embassy here, but sometimes it takes a long time for the Soviet government to tell us,`` she said.

Securing Soviet exit documents and entry visas from a Western nation usually takes a month, a U.S. Embassy spokesman said.

The spokesman declined to divulge the names of those to receive exit visas, citing rules protecting the privacy of people involved in emigration cases.

Neither of the Chicago-area residents married to Soviet citizens are on the list, according to the staff of U.S. Sen. Paul Simon (D., Ill.), who has lobbied the Soviets on behalf of divided families.

Simon Levin, 35, of Deerfield, a naturalized American citizen, was married to Tamara Tretyakova, 38, in Moscow in March, 1978. Levin has an 8-year-old son, Mark, whom he has never seen.

Fran Pergericht, 33, of Lincoln Park married Roman Kuperman, 29, also of Moscow, in February, 1982. She last saw her husband in 1985 during a vacation; she gave birth to a child earlier this year.

One of the most famous dual-nationality cases, that of Abe Stolar, 75, appeared no closer to resolution Wednesday. Stolar, born in Chicago and brought to Moscow in 1931 by his father, a devout communist, renounced his Soviet citizenship and asked to return to the U.S. in 1974.

Stolar said he had received no word from Soviet visa authorities.

State Department spokesman Charles Redman said Tuesday that Soviet officials would allow 36 familes--117 people--to join relatives abroad. Two other cases, one involving the spouse of a U.S. citizen and one a dual national, also will be resolved, Redman said.

The phrasing of the State Department announcement and information provided by those wishing to emigrate indicate that the list includes mostly

``refuseniks``--Soviet Jews previously denied permission to leave.

Soviet authorities do not recognize emigration for spiritual reasons, but consider applications from members of religious minorities requesting reunification with relatives in Western countries.

Interested Muscovites, who spent the day telephoning or criss-crossing the city seeking information, came up with a partial, unofficial list of those receiving permission to emigrate.

Several who were told they may depart have been openly active in the emigration movement. They include a former national chess champion, Boris Gulko, 38, and biologist Vladimir Apekin, 49.

Gulko has held daily demonstrations to press his emigration bid. Apekin, who will leave with his wife, daughter and granddaughter, recently became more active in the Jewish human rights movement.

Approval of their visa requests contrasts with previous Soviet policy, which did not reward activism with emigration papers, fearing it would seem the Kremlin was bowing to pressure.

Other ``refusenik`` families said to be on the emigration list include the Ozernoi family of four and the Rosen family of two.

Not all the departees, however, are Soviet Jews.

Pentacostal activist Pavel Timonin and his wife, Lyuba, will be joining family in Texas, friends and diplomats confirmed.

Timonin confided to a Western correspondent recently that he feared imminent arrest because he had been denounced in a newspaper article.

One diplomatic source with knowledge of the new emigration list said the one dual national on the list does not live in Moscow.

Western human rights analysts here agreed the Kremlin action was part of a program to improve its image. But they scoffed at suggestions that the emigration list was part of a campaign to heal public relations wounds following the April 26 disaster at the Chernobyl nuclear power plant that sent radiation spewing across Europe.

``The Soviet bureaucracy is just too big for these decisions to have been taken since then,`` said one diplomat. ``These names have been in the pipeline for a long time.``